Evidence from Discrepancies Between GPS Velocities and Rigid-Plate

GEOPHYSICAL RESEARCH LETTERS, VOL. 29, NO. 10, 10.1029/2001GL013391, 2002

Deformation of convergent plates: Evidence from discrepancies between GPS velocities and rigid-plate motions Youqing Yang and Mian Liu Department of Geological Sciences, University of Missouri, Columbia, MO, USA. Received 8 May 2001; revised 24 October 2001; accepted 14 November 2001; published 30 May 2002.

[1] Systematic discrepancies between the Global Positioning at the plate boundary, causing the coastal region to move System (GPS) site velocities and those predicted by plate-motion 30–40 mm yr1 eastward with respect to stable South America models across the Andes, the Himalayan-Tibetan plateau, and the [Leffler et al., 1997]. The GPS velocity drops gradually over the Taiwan orogen delineate diffuse plate-boundary deformation and 1000-km wide Andean orogen, indicating a crustal shortening significant intraplate deformation, even in the presumably rigid pattern significantly different from that reflected in geological record [Liu et al., 2000]. oceanic plates. The relationship between the GPS velocities and the [4] The deformation of these convergent plates can be better predictions of plate-motion models is illustrated using a simple illustrated by comparing the GPS site velocities with the predic- timescale-dependent mechanical model of plate convergence. A tions of plate-motion models (Figure 1b). The comparison is simple stiffness number (f), based on the difference between the within the same reference frame of a fixed stable South America. predictions of plate-motion models and the GPS velocity near plate For each GPS site the corresponding rigid-plate velocity was boundaries, provides a convenient measure of the ‘‘plate-like’’ calculated from the Nuvel-1A model [DeMets et al., 1994] because behavior of convergent plates and strain partitioning between of the large area spanned by the GPS sites. The Nuvel-1A intraplate and interplate deformation. INDEX TERMS: 8102 velocities are identical along the small circle around the Euler Tectonophysics: Continental contractional orogenic belts; 8158: pole for the Nazca-South America relative motion (Figure 1a), Evolution of the Earth: Plate motions—present and recent (3040) whereas along the EISL-BRAZ profile the Nuvel-1A velocities deviate <1% from that along the small circle. So the contrasts between the GPS and Nuvel-1A velocities in Figure 1a reflect 1. Introduction primarily the difference between active crustal deformation and the prediction of plate-motion models. The plate boundary is marked [2] The basic tenet of the plate tectonics theory is that tectonic by the sharp drop of GPS velocity at the trench and diffuse plates are rigid and crustal deformation is concentrated within deformation across the Andes. Note that at all four sites on the narrowly defined plate boundaries. Studies in the past decades have Nazca plate the GPS velocity is consistently lower than the proven this tenet to be essentially valid in most places, especially Nuvel-1A predictions. Because the Nuvel-1A model was based for oceanic plates. One of the most satisfying tests is the general on marine magnetic anomalies averaged over the past 3 Myr, the agreement between the Global Positioning System (GPS) velocities lower GPS velocities were explained as indications of a slowing of and the prediction of rigid-plate motion models at many parts of plate convergence [Norabuena et al., 1999]. This is best shown by the Earth’s surface [Larson et al., 1997; Stein, 1993]. However, it is the 14 mm yr1 difference between the Nuvel-1A and GPS well known that deformation diffuses over broad regions at some velocities at EISL, a GPS site near the spreading center. However, convergent plate boundaries, where the GPS velocities usually the 6mmyr1 drop of the GPS velocity from EISL to ISFE near show a systematical deviation from plate-model predictions the trench may represent intraplate shortening of the Nazca plate, [Larson et al., 1999; Leffler et al., 1997]. Here we use such because these two sites are predicted to have almost identical discrepancies across the Andes, the Himalayan-Tibetan plateau, eastward velocity in the Nuvel-1A model. Similar drop of GPS and the Taiwan orogen to illustrate diffuse plate boundary defor- velocity is found at sites IRCR and GALA but with larger errors. mation in these regions. We investigate the relationship between The corresponding strain rate is up to 7 1017 s1, comparable instantaneous and long-term averaged plate motions using a simple to that of some continental deformation. Although data from the timescale-dependent mechanical model, and discuss strain parti- Nazca plate may be too sparse to firmly delineate intraplate tioning at plate boundaries using GPS data. deformation, we show below that similar patterns of deformation are observed in other convergent plates.

2. GPS Velocities vs. Plate-Motion Model 2.2. The Himalayan-Tibetan Plateau Predictions [5] The India-Eurasia collision and continued convergence in 2.1. The Andes the past 50–70 Myr have led to the formation of the Hima- [3] The Andean mountain belt has resulted from subduction of layan-Tibetan plateau. The collisional deformation diffused thou- the Nazca plate underneath the South America plate in the past sands of kilometers into the Eurasia plate [Tapponnier and 30 Myr [Isacks, 1988]. The present-day plate convergence and Molnar, 1979]. This is clear from recent GPS measurements the Andean crustal shortening are revealed by recent GPS meas- (Figure 2a). For comparison we converted the GPS velocities urements [Angermann et al., 1999; Leffler et al., 1997; Norabuena from three groups [Chen et al., 2000; Larson et al., 1999; Wang et al., 1999] (Figure 1a). Between site EISL in the Nazca plate and et al., 1999] into those relative to stable Eurasia using the No- sites in stable South America (UEPP and BRAZ) there is Net-Rotation Nuvel-1A (NNR-A) absolute plate motion model 66 mm yr1 convergence. About half of the convergence is [Argus and Gordon, 1991]. Note the diffuse deformation over the consumed by sliding in the subduction zone and the rest is locked Tibetan plateau. [6] Figure 2b shows that the GPS velocities at the interior India (IISC) and Eurasia (IRKT) plates are almost identical to the Nuvel- 1 Copyright 2002 by the American Geophysical Union. 1A predictions. Between these two stations there is 50 mm yr 0094-8276/02/2001GL013391$05.00 N-S convergence, agreeing with the Nuvel-1A model. As the sites

110 - 1 110 - 2 YANG AND LIU: DEFORMATION OF CONVERGENT PLATES

on westerly striking planes in central India [Singh et al., 1999] including the 26 Jan. 2001 Gujarat earthquake. 2.3. The Taiwan Orogen [8] The Taiwan orogen is another example of complicated plate boundary deformation. It has resulted from convergence between the Philippine Sea and the Eurasian plates during late Cenozoic. The active mountain building is shown by the recent GPS measure- ments [Yu et al., 1997] (Figure 3). We mapped the GPS velocities onto the Eurasia-fixed reference frame by using the GPS velocity at TAIW (TAPN) [Larson et al., 1999] with respect to stable Eurasia and adding this velocity vector to the rest GPS site. The area covered by the Taiwan GPS network is small (about 2° 3°) that a uniform translation may be justifies, and there is no evidence of significant rotation of the Taiwan islands with respect to stable Eurasia. Figure 3 compares the GPS velocities with the Nuvel-1A. At Lanhsu, an island on the Philippine Sea plate, the GPS velocity is almost identical to the Nuvel-1A value. However, as the sites approach the Longitude Valley Fault (LVF), the present-day plate

Figure 1. (a) GPS sites velocities relative to stable South America (data are from Angermann et al. [1999] and Norabuena et al. [1998]). The dashed line is a small circle through EISL around the Euler pole for the Nasca-South America relative motion. Along the circle site velocities should have the same magnitude for rigid plates. The solid line shows the location of the profile in (b). (b) Comparison of the GPS velocities (black dots with error bars) with Nuvel-1A model predictions (open circles) along the EISL-BRAZ profile. All Andean GPS sites within 200 km of the profile were projected. The dashed lines fit the Nuvel-1A velocity along the small circle in (a), and the solid line fits the GPS velocities. Only the east velocity component is shown for clarity.

approach the Main Boundary Fault (MBF), the discrepancy between the GPS and the Nuvel-1A velocities increases. Across the MBF, the GPS velocity drops from 44 mm yr1 at BIRA at the northern rim of the India plate to 23 mm yr1 at LHAS in southern Tibet, representing 40% of the total N-S contraction between IRKT and IISC. The average strain rate is 1.7 1015 s1 across the Himalayan front. The rest of the convergence is distributed across the Tibetan plateau and a broad region in central Asia. The nearly linear GPS velocity change over the Tibetan plateau is similar to that over Central Andes (see Figure 1b). Some recent GPS measurements [Freymueller et al., 2000] indicate a more Figure 2. (a) GPS velocities across the India-Eurasia plate smooth velocity drop across both the Himalayas and the Tibetan boundary with respect to stable Eurasia. The dashed line is a small plateau than those shown in Figure 2b. circle around the India-Eurasia Euler pole, along the circle the [7] Besides the broad deformation within the Eurasia plate, Nuvel-1A velocity has the same magnitude. The solid line shows Figure 2b also indicates significant shortening within the India the location of the profile in (b). Nuvel-1A velocities along this plate, the rigid indenter. Between IISC and the northern rim of the profile deviate <2% from that on the small circle. (b) Comparison India plate (sites MAHE, NEPA, and others) there is about 4 mm of the GPS site velocities (black dots with error bars) with the yr1 shortening, indicating a strain rate of 8 1017 s1. The Nuvel-1A velocities (open circles) along a profile from IISC to corresponding N-S compression within the interior of the India IRKT. GPS sites within a 200 km swath along the profile are plate are consistent with the predominately thrust-fault earthquakes projected. Only the north component is shown for clarity. YANG AND LIU: DEFORMATION OF CONVERGENT PLATES 110 - 3

The corresponding displacements are shown in Figure 4c. The displacement of plate 2 near the boundary zone, U2 , increases at the velocity V2 when stress is accumulating but drops to zero when a sliding event occurs. The displacement of plate 1 near the boundary zone, U1, increases at the velocity V1 but jumps up each time when a slip occurs at the plate boundary. The long-term averaged U1 would approach V0t. In other words, the long-term averaged GPS velocity would approach that of the rigid-plate

Figure 3. Comparison of GPS velocities in Taiwan area with Nuvel-1A predictions. The GPS data (from Yu et al. [1997]) are adapted to the Eurasia-fixed reference frame, projected onto the MERK-Lutao profile (see inset) for all sites within an 82-km wide swath. Negative value represent northwestward velocity compo- nent parallel to the profile. The dashed lines are Nuvel-1A velocities for the Philippine Plate with respect to fixed Eurasia. LVF: the Longitude Valley Fault; CKF: the ChuKou Fault.

boundary, the GPS velocity changes sharply. At the Coastal Range the GPS velocity differs nearly 16 mm yr1 from the Nuvel-1A predictions, indicating shortening within the Philippine Sea plate at a strain rate of 6 1015 s1, much larger than that across the Himalayan front. The active plate boundary at the LVF is marked by a sharp change (over 30 mm yr1) of the GPS velocities. However, deformation in the plate boundary zone is complicated and diffuse. Little deformation occurs within the Central Range, as indicated by the uniform GPS velocities, whereas about 20 mm yr1 velocity changes over the Chu-Kou Fault (CKF). To the west of CKF, the GPS velocity changes gradually, indicating a broad zone of crustal shortening in the Western Foothills and the Coast Plain.

3. Discussion

[9] The diffuse plate-boundary deformation and significant intraplate deformation in the three pairs of convergent plates deviate from the paradigm of the plate tectonics theory. However, the plate tectonics theory is based on geological records spanning over millions of years, whereas the GPS data were collected over a period of several years. The relationship between transient stain and permanent deformation across convergent plates can be illustrated using a simple mechanical model (Figures 4a–b). This model provides a first-order approximation of the mechanical behavior of convergent plates: permanent crustal shortening (vis- cous flow in the dashpot) in collisional boundary zone, elastic deformation within the plates (springs), and plastic slipping (slid- Figure 4. A mechanical model for the deformation of a pair of ing along subduction zone) when tectonic stresses reach the yield convergent plates. (a) Sketch of the convergent plates. (b) The strength of the crust. When the system is compressed from the left mechanic model: springs represent tectonic plates, sliding at the end of the model at a constant velocity V0 with respect to the fixed plate boundary are represented by the frictional plates, and right side, the stress s(t) increases with time: s(t)=sb +(V0h /d permanent deformation at the boundary zone is represented by sb)[1 exp((d/h /(L1/E1 + L2/E2))t)] , where sb is the background viscous flow in the dashpot. Convergence of the plates is simulated stress, t is time, d and h are the width and viscosity of boundary by fixing the right end and moving the left end at velocity V0. (c) zone, L1, E1, L2, and E2 are the length and elastic moduli of plates 1 Solid lines show the predicted displacements of plates 1 (U1) and 2 and 2, respectively. Assuming the viscous dashpot is stronger than (U2) near the boundary zone. Dashed line shows the rigid-plate the sliding plates, i.e., the maximum viscous stress V0h /d > sy, model predictions. (d) The velocity profiles for the mechanical which is the yield strength of the sliding plates, then whenever the model (thick solid lines), the rigid-plate model (thick dashed lines), stress in the system reaches sy, sliding occurs between the frictional and the extreme case when the two plates have identical rheology plates, the stress drops to sb , and the process then repeats. and are completely coupled (thin dashed lines). 110 - 4 YANG AND LIU: DEFORMATION OF CONVERGENT PLATES

and the long-term geological records. Results of this study should be useful for studies of plate boundary deformation in other regions.

[13] Acknowledgments. We thank Z.-K. Shen for providing unpub- lished GPS data of central Asia, and Tim Dixon for providing a preprint. We benefited from discussion with Seth Stein, Tim Dixon, and Z.-K. Shen, and constructive criticism by an anonymous GRL referee. This work was supported by NASA grant NAG5-9145 and NSF grant EAR-9805127.

References Angermann, D., J. Klotz, and C. Reigber, Space-geodetic estimation of the Nazca-South America Euler vector, Earth Planet. Sci. Lett., 171, 329– 334, 1999. Argus, D. F., and R. G. Gordon, No-net-rotation model of current plate velocities incorporating plate motion model NUVEL-1, Geophys. Res. Lett., 18, 2039–2042, 1991. Chen, Z., B. C. Burchfiel, Y. Liu, R. W. King, L. H. Royden, W. Tang, Figure 5. Stiffness number (f) of the plates in this study. Solid E. Wang, J. Zhao, and X. Zhang, Global positioning system measure- bars are oceanic (or part of oceanic) plates. Empty bars are ments from eastern Tibet and their implications for India/ Eurasia continental (or part of continental) plates. CR: Coastal Range. intercontinental deformation, J. Geophys. Res., 105, 16,215–16,227, 2000. DeMets, C., R. G. Gordon, D. F. Argus, and S. Stein, Effect of recent motion models. V1 and V2 are the instantaneous velocities of the two plates near the boundary zone that would be reflected in GPS revisions to the geomagnetic reversal time scale on estimates of current plate motion, Geophys. Res. Lett., 21, 2191–2194, 1994. measurements. For this model their values depends on the con- Freymueller, J. T., Z. Yang, Q. Wang, R. Bilham, R. Bendick, K. M. vergence rate and the rheology of the plates: V1 = V0 kL1/E1 and Larson, Q. Chen, C. Xu, W. Jiang, and J. Liu, New Kinematic Data from V2 = kL2/E2, where k (V0 sbd/h)/(L1/E1 + L2/E2) when t < h/ Asia: Implications for Dynamic Models, Eos Trans. AGU, 81, F1226, Max(E1, E2). 2000. [10] The instantaneous velocity profile of the model (Figure Isacks, B. L., Uplift of the central Andean plateau and bending of the Bolivian orocline, J. Geophys. Res., 93, 3211–3231, 1988. 4d) is consistent with the GPS velocities across the convergent Larson, K., R. Burgmann, R. Bilham, and J. T. Freymueller, Kinematics of plate boundaries (see Figures 1–3). The deviation of the GPS the India-Eurasia collision zone from GPS measurements, J. Geophys. velocities from those of plate-motion models depends on the Res., 104, 1077–1094, 1999. rheology of the convergent plates and the degree of mechanical Larson, K. M., J. T. Freymueller, and S. Philipsen, Global plate velocities coupling between the plates. To quantify the non-rigid behavior from the Global Positioning System, J. Geophys. Res., 102, 9961–9981, 0 1997. of the plates we define a stiffness number, f: f =(V Vg)/ 0 Leffler, L., S. Stein, A. Mao, T. Dixon, M. Ellis, L. Ocala, and I. S. Sacks, (V Vp), where Vg is the instantaneous or the GPS velocity Constraints on the present-day shortening rate across the Central Eastern near the plate boundary zone, Vp is the velocity at the same Andes from GPS measurements, Geophys. Res. Lett., 24, 1031–1034, location predicted by plate-motion models, and V 0 is the 1997. velocity we would have at the same location if the plates Liu, M., Y. Yang, S. Stein, Y. Zhu, and J. Engeln, Crustal shortening in the are completely coupled so that there is no plate boundary (see Andes: Why do GPS rates differ from geological rates?, Geophys. Res. 0 Lett., 27, 3005–3008, 2000. Figure 4d). For this model V = V0(L2 + d)/L for plate 1 and 0 Norabuena, E., L. Leffler-Griffin, A. Mao, T. Dixon, S. Stein, I. S. Sacks, V = V0L2/L for plate 2, here L = L1 + d + L2. When Vg = Vp, L. Ocala, and M. Ellis, Space geodetic observations of Nazca-South f = 1 and the plate behaves as the perfect rigid plate assumed America convergence along the Central Andes, Science, 279,358– 0 in classical plate tectonic theory. To the other end, Vg = V and 362, 1998. f = 0 when the two plates have identical rheology and are Norabuena, E. O., T. H. Dixon, S. Stein, and C. G. A. Harrison, Decelerat- completely coupled, so the only strain is intraplate. For ing Nazca-South America and Nazca-Pacific plate motions, Geophys. Res. Lett., 26, 3405–3408, 1999. convergent plates f provides a measure of their stiffness, or Stein, S., Space geodesy and plate motions, in Space Geodesy and Geody- their ‘‘plate-like’’ behavior. Figure 5 shows the f values of the namics, edited by D. E. Smith and D. L. Turcotte, pp. 5–20, American plates in this study. As expected, the oceanic plates have high Geophysical Union, Washington, D. C., 1993. f values, whereas the central Asia and Taiwan have low f Singh, S. K., M. Ordaz, R. S. Dattatrayam, and H. K. Gupta, A spectral values. Note that stable South America and the India plate are analysis of the 21 May 1997, Jabalpur, India, earthquake (Mw = 5.8) and stiffer than the oceanic Nazca plate. estimation of ground motion from future earthquakes in the Indian Shield region, Bull. Seismo. Soc. Am., 89, 1620–1630, 1999. [11] The f value also provides a direct measure of intraplate Tapponnier, P., and P. Molnar, Active faulting and Cenezoic tectonics of strain rate relative to the total strain rate across the convergent Tien Shan, Mongolia and Baykal regions, J. Geophys. Res., 84, 3425– plates. AsÀÁ shown in Figure 4d, the intraplate strain rate of plate 1 3459, 1979. is e_ ¼ V0 Vg L1, whereas the theoretical maximum is Wang, M., Z.-K. Shen, D. Jackson, A. Yin, Y. Li, C. Zhao, D. Dong, and e_ ¼ ðÞV V 0 =L . By the definition of f we have e_=e_ P. Fang, GPS-derived deformation along the northern rim of the Tibe- max 0 1 max tan plateau and southern Tarim basin, Eos Trans. AGU, 80, F1009, =1 f. Thus f = 0.8 for the India plate, for instance, means that 1999. the intraplate strain rate is about 20% of the total strain rate across Yu, S. B., H. Y. Chen, and L. C. Kuo, Velocity field of GPS stations in the the India plate and that the remaining 80% is consumed by plate Taiwan area, in An introduction to active collision in Taiwan, pp. 41–59, boundary deformation. Elsevier, Amsterdam, Netherlands, 1997. [12] GPS and other space-based geodetic measurements are playing an increasingly important role in tectonic studies. Inter- pretation of the tectonic significance of GPS data, however, requires a good understanding of the relationship between Y. Yang and M. Liu, Department of Geological Sciences, University of instantaneous crustal deformation reflected in most GPS data Missouri, Columbia, MO 65211, USA. ([email protected])